the-circle-with-a-radius-of-one-unit-is-partitioned-into-eight-equal-arcs-where-

Question

The circle with a radius of one unit is partitioned into eight equal arcs, where each arc corresponds to specific values. Determine the value of the trigonometric function at the given real number using the (x,y) coordinates in the diagram or specify that the expression is undefined.

$\cot(\frac{5\pi}{4})$

Unit circle with coordinates for trigonometric functions, showing angles and values.

$\cot(\frac{5\pi}{4})$

Accepted Answer

﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math>1﻿

Answer

﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{\sqrt2}{2}</annotation></semantics></math>22<svg width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
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s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg>​​﻿

Answer

﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">-\frac{\sqrt2}{2}</annotation></semantics></math>−22<svg width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
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c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
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c69,-144,104.5,-217.7,106.5,-221
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Answer

﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">-1</annotation></semantics></math>−1﻿